We detect dipping activity/modulations in the light curve of the four low-mass X-ray binaries in the 3-10 keV and 20-40 keV energy ranges. The spectral parameters derived from the fits to the International Gamma-Ray Astrophysics Laboratory data are consistent with hot coronal structures in these systems where we find a range of plasma temperatures 3.0-224.9 keV. The unabsorbed X-ray to soft gamma-ray fluxes between 4 keV and 200 keV are 5.9 x 10(-10) erg s(-1) cm(-2) for XB 1916-053, 3.3 x 10(-10) erg s(-1) cm(-2) for XB 1323-619, 21.6 x 10(-10) erg s(-1) cm(-2) for X 1624-490, and 11.0 x 10(-10) erg s(-1) cm(-2) for 4U 1746-371. The optical depth to Compton scattering, tau, varies in a range 4.4-0.002 consistent with electron densities n(e) < 1.4 x 10(15) cm(-3). In general, we find no significant difference in the dip and non-dip spectra in the ISGRI energy range (above 20 keV) for all the four sources. We only detect absorption differences between dipping and non-dipping intervals for XB 1916-053 and X 1624-490 in the JEM-X energy range. Fits in the 4-200 keV range including an additional photoionized absorber model for the two sources show that XB 1916-053 has the highest ionized absorber among the two.